Science:Math Exam Resources/Courses/MATH101/April 2006/Question 03 (c)
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Question 03 (c) 

FullSolution Problems. Justify your answers and show all your work. Simplification of answers is not required. Evaluate the following integral. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Try a trig substitution. 
Hint 2 

Try the trig substitution 
Hint 3 

Later down the road you may want to use

Hint 4 

Don't forget to plug back your original variables. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Let so that . Then we have
Now we isolate for the original variables. Using the diagram below (created from noting the original condition on x and by using Pythagorean theorem), we have
completing the proof. 